A341613 - OEIS

%I #9 Feb 22 2021 14:25:17

%S 0,0,0,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,

%T 1,0,0,0,1,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,1,

%U 1,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1

%N Characteristic function for A341615: a(n) = 1 if sigma(n) < 2n < A003961(n), otherwise 0.

%H Antti Karttunen, <a href="/A341613/b341613.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A252742(n) * A294934(n).

%F a(n) <= A341612(n).

%t f[1] = 1; f[n_] := Times @@ (NextPrime[#1]^#2 & @@@ FactorInteger[n]); a[n_] := Boole[DivisorSigma[1, n] < 2*n < f[n]]; Array[a, 100] (* _Amiram Eldar_, Feb 22 2021 *)

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A341613(n) = ((sigma(n)<(2*n))&&((2*n)<A003961(n)));

%Y Cf. A000203, A003961, A252742, A294934, A341613, A341614.

%K nonn

%O 1

%A _Antti Karttunen_, Feb 22 2021